The official, speaking on condition of anonymity, said US President Joe Biden has been briefed regularly on the threats and has directed his team to address Iranian plots against Americans.
At Biden's direction, top US officials have sent messages to the highest levels of the Iranian government warning Tehran to cease all plotting against Trump and former US officials, the official said.
The Iranians have been told Washington would view it as an act of war if any attempt was carried out against Trump's life, the official said.
Iran has denied interfering in US affairs. Tehran, in turn, says Washington has interfered in its affairs for decades, citing events ranging from a 1953 coup against a prime minister to the 2020 killing of its military commander in a US drone strike.
In January 2020, Trump ordered a US air strike that killed Iran's then-top military commander, Qassem Soleimani, after receiving intelligence that Soleimani was planning imminent attacks on US diplomats and armed forces in Iraq, Lebanon, Syria and elsewhere in the Middle East.
Trump is now seeking a return to the White House after losing the 2020 election to Biden.
Trump ordered the US air strike that killed Iran's top military commander Qassem Soleimani in 2020. (AP PHOTO)
He is in a battle against Vice President Kamala Harris in the race to win the November 5 election.
Trump's campaign said on September 24 the former president was briefed by US intelligence officials on the alleged threat from Iran.
The White House said the United States has been closely tracking Iranian threats against Trump for years and it warned of "severe consequences" if Tehran was to attack any US citizen.
"We consider this a national and homeland security matter of the highest priority, and we strongly condemn Iran for these brazen threats," White House National Security Council spokesman Sean Savett said.
"Should Iran attack any of our citizens, including those who continue to serve the United States or those who formerly served, Iran will face severe consequences."
He said "appropriate agencies are continuously and promptly providing the former president's security detail with evolving threat information".
"Additionally, President Biden has reiterated his directive that the United States Secret Service should receive every resource, capability, and protective measure required to address those evolving threats to the former president," Savett said.
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